Flop and roll: Learning robust goal-directed locomotion for a Tensegrity Robot

Model-Predictive Control With Inverse Statics Optimization for Tensegrity Spine Robots

“…The optimization problem of eqn. (27)(28)(29) is the standard form of tensegrity inverse kinematics as used in [20], [21]. If a feasible q is found, the rest lengths ρ i of each cable i ∈ {1, ..., s} are back-calculated from eqn.…”

“…Model-based closed-loop control has been mostly limited to low-dimensional structures [23], [24], [25], [13], [26]. More complex and high dimensional systems have been addressed with model-free methods [16], [22], [18], [27], [28], [29] or open-loop control [30], [31], [32], [20]. In order to use a tensegrity spine with Laika, a model-based closed-loop tracking controller was developed by the authors in [12] and is improved upon in this work.…”

“…(27)(28)(29), in the context of robotics and control systems, did not address these rank issues when implemented for this 2D spine. Reducing (27)(28)(29) to a cablesonly formulation by optimizing only over q s as suggested in [20] only exacerbates these rank issues by defining A with fewer columns. Additionally, the relaxation of this equalityconstrained problem to an inequality-constrained formulation, as used in [20], did not make the problem feasible.…”

“…Finally, since states {ξ (3) , ξ (15) , ξ (27) } are the vertebra z-positions, constraints (65-66) prevent vertebra collisions.…”

“…This rigid body formulation (eqn [32][33][34][35][36][37][38][39][40][41][42][43]. can be combined with the minimum force density optimization problem (eqn [27][28][29]. by substituting the equality constraints, as in…”